two trapezoids make a parallelogram
Here are two congruent trapezoids. Draw them together so that
they form a single parallelogram.
Parallelogram width = trapezoid lower base + trapezoid upper base
The parallelogram is made up of two trapezoids. This means that the area of each trapezoid
must be half that of the parallelogram, and we know that the area of a parallelogram is equal to
height x width.
What’s the width of the parallelogram?
The trapezoid upper and lower bases added together.
What’s the height of the parallelogram?
The trapezoid height
What ideas do you have about how to calculate the area of a trapezoid?
Sp
in one of the
trap
ezoids 180˚ and
y
ou can fi
t them
both t
ogether to
f
orm a para
llelogram.
=
trapezoid height
Parallelogram height
Calculate trapezoid area using
base length and height
So what we’ve discovered is that, like with the other
shapes you’ve encountered so far, there’s a shortcut
we can take if we want to find the area of a trapezoid.
All we need to do is add together the upper and lower
base lengths, multiply by the height, and then divide
by two.
2
Trapezoid Area = height (base 1 + base 2)
264 Chapter 6
quadrilaterals
What’s the charge for maintaining the trapezoid lawn? Thankfully, Ed went back and collected
some extra measurements to help you out with the perimeter.
28 meters
25 meters
30 meters
24 meters
53 meters
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exercise solution
What’s the charge for maintaining the trapezoid lawn? Thankfully, Ed went back and collected
some extra measurements to help you out with the perimeter.
24 meters
28 meters
53 meters
25 meters
30 meters
Trapezoid area = 1/2 x 24 x (28 + 53)
= 12 x 81
= 972 meters
2
Trapezoid perimeter = 28 + 30 + 53 + 25
= 136 meters
Maintenance charge = $0.05 x 972 + $0.10 x 136
= $48.60 + $13.60
= $62.20
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quadrilaterals
The Trapezoid Exposed
This week’s interview:
What’s So Special About Trapezoids?
Head First: Hey, Trapezoid, nice to have you on
the show tonight.
Trapezoid: It’s a real pleasure. I don’t seem to get
out as much as some of the other shapes.
Head First: What do you mean?
Trapezoid: Well, everyone knows about Square and
Rectangle, although they’re kind of boring if you
ask me. Kite gets good press because it looks like…
well…a kite. But me? Everyone forgets about me.
Head First: I notice that you didn’t mention
Parallelogram. Don’t you guys have something in
common?
Trapezoid: Some would say we’re family, and I
guess you could say we’re kinda like cousins. I have
only one pair of parallel sides, and Parallelogram
has two. But don’t you think that’s just being greedy?
Parallelogram’s just a lopsided, funny-looking
Rectangle if you ask me, and I don’t limit myself like
that.
Head First: But aren’t you just like Triangle but
with one of the points chopped off ?
Trapezoid: That’s one way you could talk about
me, yes, but the key thing is that I have one pair of
parallel sides, and Triangle doesn’t. Um, I wouldn’t
talk to Triangle about that, he’s still a bit sensitive.
Head First: But don’t you have one nice thing in
common with Triangle?
Trapezoid: You did your research, didn’t you?
We’ve all heard of an Isosceles Triangle, right? Well,
Trapezoids can be Isosceles, too.
Head First: What’s special about that?
Trapezoid: It’s still a Trapezoid, but with congruent
legs. And by legs I mean the sides that aren’t bases.
Isosceles Trapezoid is a bit more regular than me,
there’s more symmetry about him. He’s thinking
about getting into modeling, from what I hear. At the
very least, it must make shaving much easier.
Head First: What about diagonals?
Trapezoid: What about them? Sure, I have them,
but I can’t say much about them. Now Isosceles
Trapezoid, he has congruent diagonals, and he has
some congruent angles, too. Some guys have all the
luck.
Head First: Well, that’s all we have time for,
Trapezoid, thanks for stopping by.
A trapezoid is a four-sided shape
with one pair of parallel sides called
bases.
Since the bases are parallel, this
means that you have two pairs of
supplementary angles.
An isosceles trapezoid is a trapezoid
with congruent “legs.” The lower
base angles are congruent, the upper
base angles are congruent, and the
diagonals are congruent, too.
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